报告名称：Relational Marginal Problems: Theory and Estimation

主办单位：数学与统计学学院

报告专家：Yuyi Wang（王彧弋）

专家所在单位：瑞士苏黎世联邦理工学院

报告时间：2019年4月18日(周四)上午10:30-12:00

报告地点：数学与统计学学院201报告厅

专家简介：王彧弋 博士，苏黎世联邦理工学院博士后研究员，于2015年从比利时鲁汶大学获得博士学位，2011年从新加坡国立大学获得硕士学位，2009年本科毕业于华中科技大学。现在的研究兴趣包括理论计算机科学和机器学习，发表了30余篇学术论文，并且在FOCS，AAAI，IJCAI，UAI，FC和WINE等顶级学术会议做报告。理论计算机关注在线计算、分布式计算和并行计算。机器学习方面则更注重统计学习理论，尤其是关系型数据（非i.i.d.）上的学习理论。

报告摘要：In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two different notions of relational marginals. Second, we show a duality between the resulting relational marginal problems and the maximum likelihood estimation of the parameters of relational models, which generalizes a well-known duality from the propositional setting. Third, by exploiting the relational marginal formulation, we present a statistically sound method to learn the parameters of relational models that will be applied in settings where the number of constants differs between the training and test data. Furthermore, based on a relational generalization of marginal polytopes, we characterize cases where the standard estimators based on feature’s number of true groundings needs to be adjusted and we quantitatively characterize the consequences of these adjustments. Fourth, we prove bounds on expected errors of the estimated parameters, which allows us to lower-bound, among other things, the effective sample size of relational training data.